Wednesday, October 31, 2012

What, if some day or night a demon were to steal after you into your loneliest loneliness and say to you: "This life as you now live it and have lived it, you will have to live once more and innumerable times more; and there will be nothing new in it, but every pain and every joy, and every thought and sigh and everything unutterably small or great in your life will have to return to you, all in the same succession and sequence? -- even this spider and this moonlight between the trees, and even this moment and I myself. The eternal hourglass of existence is turned upside down again and again, and you with it, a speck of dust!"

Would you not throw yourself down and gnash your teeth and curse the demon who spoke
thus? Or have you once experienced a tremendous moment when you would have answered him: "You are a god and never have I heard anything more divine." If this thought gained possession of you, it would change you as you are or perhaps crush you. The question in each and every thing, "Do you desire this once more and innumerable times more?" would lie upon your actions as the greatest weight. Or how well disposed would you have to become to yourself and to life to crave nothing more fervently than this ultimate eternal confirmation and seal? (Gay Science 341, Kaufmann trans.).

Unlike some readers of Nietzsche, I'm inclined to think Nietzsche intended his remarks about eternal recurrence not as a mere thought experiment but rather as a genuine cosmological possibility. His unpublished reflections on eternal recurrence suggest a view not unlike that of his contemporary, physicist Ludwig Boltzmann. In a universe of finite relevantly different combinatorial possibilities, infinite duration, and some means of avoiding permanent collapse into entropy, it is plausible to think that eventually the current configuration of the world will recur, not just once but infinitely often. And if one adds determinism to the picture (as most would have done in the 19th century), then once the current configuration recurs, the same subsequent states will follow. Voila, eternal recurrence.

Now update to the early 21st century by adding multiverse theory and randomness. What do we get? Eternal recurrence scrambled sideways! Sideways because the infinitely many duplicates of you need not exist only in your past and future (and in fact probably don't, assuming a finite or entropy-collapsing observable universe and universe-local spacetime) -- rather they exist "sideways", outside of our observable universe. And scrambled because rather than being destined always to play out the same, every finite possibility is played out, infinitely often.

So, on this view -- which is well within the range of the mainstream options in contemporary scientific cosmology -- there are infinitely many "Eric Schwitzgebel"s in infinitely many universes who have lived their lives identically to mine up to this minute. Given that there is a huge variety of highly improbable but finitely probable weird futures for these Eric Schwitzgebels, infinitely many Eric Schwitzgebels play out each of these weird outcomes. Infinitely many of my up-to-now counterparts decide to leave philosophy forever to pursue a hopeless career in football, infinitely many leap to death from the top of the tower, infinitely many spend the rest of the week stapling pages of Kant's first critique atop relevant passages of Hume's Treatise. And of course infinitely many also finish this blog post, in every possible way it might be finished.

How should I feel about these counterparts of mine, assuming such a cosmology is the correct one, as seems possible? They are oddly close to me, in a way, though universes distant. I can't quite find myself indifferent to them -- just as Nietzsche can't find himself indifferent to his future counterparts who must live out his every decision. Though it seems weird to say so, I find myself feeling sorry as I imagine their sufferings. I don't feel the heavy weight of Nietzsche's eternal recurrence, though. I'm not sure I would feel that weight even on Nietzsche's original assumptions, but definitely not now. Maybe instead there's a lightness: Even if I decide wrong, there will be infinitely many Erics who get it right! Conversely, there's an eeriness too: Infinitely many Erics bashed their cars headlong into that oncoming traffic.

Maybe I shouldn't take such reflections very seriously. The cosmology might not be correct. Even if it is correct, I'm the only Eric Schwitzgebel, UC Riverside philosopher, in this universe, and I really shouldn't care at all about what transpires in other universes, no matter how eerily similar. Should I? There are plenty of other people, right here on our own Earth, past and future, whom I should care about more, right? Because they're... well, why exactly? Because they're closer?

49 comments:

Although I take the Boltzmann version of eternal recurrence very seriously, I find myself very unwilling to swallow the many-worlds interpretation of quantum mechanics. Mainly because there's no postulated mechanism driving the division of the universe. Not to mention that whole falsifiability/empirical support thing...

That said, if we were to somehow be able to prove many-worlds, it would be very interesting to me. Somehow, my consciousness ends up HERE instead of THERE (a near infinite number of times per second, since we're counting decoherence events). How is that path carved? Is it directed? Is there some kind of strange temporality to it, where in some sense I am simultaneously conscious in all these parallel worlds but not aware of it yet?

I haven’t given the eternal recurrence extensive thought, usually dismissing it as a peculiar tangent in Nietzsche’s philosophy, but upon reading your article I do have some thoughts on the matter.

In the eternal return, I take Nietzsche to suggest that he’s searching for something that can ground certain norms about how we should act. Thinking about the eternal return is supposed to somehow wake us up, make us care about our lives in a certain way, and therefore influence how we act. I agree with you that it doesn’t seem convincing that we should care about our possible selves (either in parallel or in the future and past), especially when compared to other things we should care about (like other humans who are here now).

However, I don’t think Nietzsche ultimately wants us care about our alternate selves but instead to care about our self that is here and now. So although his eternal return may suggest that we should care about what we do now because it will be inscribed in what we do later (when we eternally recur), what he ultimately wants to establish (by making us care about our possible selves) is care toward our self here and now.

A lot of people seem to care about their self that is here and now (and I don’t suppose they would be searching for a way to give their life meaning; they already seem to find meaning in their lives), so I suppose Nietzsche must be addressing only the audience of pessimists and nihilists who are having trouble finding meaning in life. Perhaps he even hopes to wake up both those who believe in religious mythology and those who find hedonistic pleasures sufficient for the enjoyment of life to the triviality of their meaning and to the existential crisis that he seems to be trying to cope with.

The eternal return seems bound up both with (1) notions of our existence across time (and could possibly be extended to our existence across location, as you point out) and with (2) existential contemplation about the meaning of life (or purpose in living). Using this thought about our existence across time (and location) is somehow supposed to provide the sort of norm giving meaning about how we should act. Our attitudes about how we ought to act in this life must be somehow altered by recognition of the eternal return.

Trying to make sense of this, there is an earlier aphorism that deals with existential issues of time and meaning:

The new fundamental feeling: our permanent transitoriness. — Formerly one tried to get a feel for the majesty of human beings by pointing backward toward their divine descent: this has now become a forbidden path, because before its gate stands the ape along with other heinous beasts, grinning knowingly as if to say: no farther here in this direction. So, one has a go of it now from the opposite direction: the path humanity pursues shall serve as proof of its majesty and kinship to God. Alas, this too leads nowhere! At the end of this path stands the funeral urn of the last human and gravedigger (with the inscription “nihil humani a me alienum puto [nothing human is foreign to me]”). (Dawn 49)

Here Nietzsche tries to dispel two attempts to find existential meaning: one that looks backwards and another that looks forward. Looking backward fails, according to Nietzsche, because we descend from apes and not God (according to Darwin’s evolutionary theory and opposing the Old Testament genesis story). Looking forward fails, as well, because instead of some hidden teleology and ultimate eternal life we find ourselves with no future humanity; the impending extinction of humanity takes away meaning from our present efforts (since none will be around to either benefit from or remember our efforts). Compare despair over such fate in the book turned film Children of Men and Scheffler’s recent, related Tanner Lectures http://philosophy.fas.nyu.edu/docs/IO/4864/SchefflerTannerLectures.pdf (in which he references the former book and film).

In the face of this existential crisis, we might nevertheless become like Agathon or Rilke and try finding meaning in that our efforts will be forever inscribed in the past. Agathon, as quoted by Aristotle in the Nicomachean Ethics, says, “For this alone is lacking even to god, To make undone things that have once been done”. Rilke writes in his ninth Elegy, “And we, too, once. And never again. But this – having been once on earth – can it ever be undone?” Together, these poets express the immutability of things past, and Rilke seems to draw existential meaning from this.

So why doesn’t Nietzsche simply do something like this and try to find meaning in the immutability of the past? Either he overlooked this option or he believes that the past can only matter to us if it will happen again. We are supposed to be struck by a sort of conscience about our present actions because what falls in the past will somehow recur in the future. Perhaps this is Nietzsche best jab against nihilism (at least during the period from 1881-1885) which divines no purpose from the past and sees no future for humanity. Perhaps he thinks we should care about our present self because we would, through recognition of the eternal return, care about imprisoning our future self in our present choices. Because one day that future self will be us.

Perhaps our sense of self from one moment to the next should be just as attached to our well-being as our sense of self from the present self to the future, eternally recurred self? Somehow we’re supposed to identify with this projection of our eternally recurring self through, what?, some bizarre causal connection to our future self? If that connection amounted to the supporting force behind Nietzsche’s employment of the eternal return, then perhaps he wouldn’t care about our self in another universe (since we stand in no causal connection to that self). Perhaps Nietzsche wants us to care about our self here and now because one day our future self will be our here and now. I’m really not sure, and I think to myself that Nietzsche probably didn’t understand how to reason through his own intuitions on the eternal recurrence as well, and that later he looks to other means for overcoming nihilism.

If every possibility is played out simultaneously it's unclear to me in what meaningful sense it can be still said to be "me" in the midst of all these actualisations. Doesn't the scrambling necessitate the impossibility of any connecting "me" within all these events?

The idea of the ER is first referenced by Nietzsche in the History Meditation (2) and is attributed to the Pythagoreans; and there, as later, the fundamental idea for Nietzsche is not the physics, but our capacity (or incapacity), to digest as much (or as little) of existence, as it impinges on us.

The fact that the demon in GS.341. offers this information in your "loneliest loneliness" is no accident. It already presupposes a certain kind of suffering and alienation on the part of the reader, and readers very differently disposed are unlikely to respond to the ER in the same manner.

There are an infinite number of clasqm's who bought Apple stock when it was floating around $10 a share. If each of them transferred $1 to this universe I could *buy* this universe. But since they show no inclination to do so, and like this universe's Nobel Prize Committee, continue to feign ignorance of my existence, I shall return the compliment and not spend too much time and energy caring about them. After all, if Nietzsche was right, I will then spend an infinite number of times caring about them fruitlessly.

BTW, my learned friends, is there any reason why the sideways infinitude necessarily cancels out the longitudinal one? That seems to be an unspoken assumption here. Is it possible that there is an eternal recurrunce in each of these infinite universes? My alleged mind declares itself well and truly boggled.

Interesting reflections, Carlos. I'm inclined to agree that Nietzsche wouldn't want to hang a lot on any profound altruistic(?) concern we have for these future selves. The *primary* function of the eternal recurrence might be as a way of bringing forward a way of thinking about whether one would say "yes" or "no" to life, if you had to live it all again. The ideal of course be to live so that you would say "yes!" If it's also simply true, cosmologically, then that "yes" is somehow amplified by being a "yes" for not only me but also on behalf of all my counterparts.

David: I agree that they're not me, just my "counterparts", for whatever that's worth. And it's an open question how much that's worth. On the loneliness frame. It's interesting that it's there, and not I think meaningless, but other mentions of the recurrence are not similarly framed so I would prefer a light interpretative touch with it.

Yes, because it's physics, either classical, quantum, string theoretic, etc., that tells us that sequences can be multidirectional but not reversible. And sequences that go back infinitively will not logically have come back in some exact parallel. But illogically o course, they can.

What I should have added is that when you have these examples where some parts are naturally out of sequence from some "parallel" set of changes, finding parts of those same sets to be in the exact "web" of sequence of our sets is even more bazaar, since they'd have no causative history that could account for the phenomena. The theory that "anything can happen" is essentially based on hope that impossible accidents are not impossible.

Eric: True, but the loneliness issue is practically omnipresent in Nietzsche, both personally and philosophically; in his views on language and consciousness etc, and the idea that:"For me - how should there be any outside-myself? There is no outside. But all sounds make us forget this; how lovely it is that there are sounds"(TSZ.III.13).

This is not solipsism he's affirming, but the uncrossable gap that necessarily exists between the self and any other, no matter how empathetic either may be. And this gap, I would argue, is a source of persistent suffering for Nietzsche, and hence is a significant part of the pain that the ER is trying to affirm. This separation is part of what the Dionysian myth of wholeness and unity seeks to obliterate.

Again, I'm emphasising Nietzsche's own relation to the ER and paying little attention to what others make of it.

I once heard something like Anonymous' point explained to me this way. (To be sure, this is an over-simplification, but it may help us non-specialists.) Suppose you take the numeral for pi, and delete all the '3's after the decimal point. Then, even though '3' occurs once before the decimal point, it never occurs again...even though the sequence after the decimal point remains infinite.

The eternal return is a means of clearing our creative here-now of past things in order to open more "space" to things over which our will can have an influence.

The eternal return is the willing of the indefinite repetition of the conditions that made possible the emergence of the will so that it has the possibility of emerging in the future. In a chaotic universe (sensitive to initial conditions) one would have to will the indefinite repetiton of everything in order for this to be possible.

If I'm remember aright, your view isn't so different from Kundera's account of Eternal Return in The Unbearable Lightness of Being, Eric.

I've always read Nietzsche as attempting to chase the logic of the Enlightenment to its conclusion - nihilism - and the Eternal Return as precisely the kind of cosmological theses the Enlightenment has made possible, such as those falling out from brane theory and so on.

In this sense, he's anticipating what Freud would call the 'third great narcissistic wound' a couple of decades after, the fall of 'noocentrism' in the wake of the fall of biocentrism (Darwin) and geocentrism (Copernicus) from cognitive grace.

The enemy here is nothing less than Enlightenment reason - so the question is one of what to posit in its wake, if all it delivers is the ultimate dissolution of human value. Nietzsche offers an irrational response - (crudely) affirmation for affirmation's sake - and the Eternal Return provides him with the dramatic background he needs to convey the stakes.

It's this 'dehumanizing (decentralizing) background' that's the important thing. What does it mean to affirm value against such a background? That's the question.

It's hokey to be sure. And I can't help but think if he were around today, if he could see how thoroughly cognitive science has confirm, even surpassed his pessimistic predictions, he'd be playing online video games.

Scott Bakker: No, the "nihilistic" problem is essentially visceral, characterological, and not conceptual.

The advocates of the Last Man, the overwheliming majority of humanity, find no difficulty in affirming values and existence in a Godless universe. The enemy isn't Enlightenment Reason, this enlightenment allows them to take a pleasantly ironic view of themselves.

What we also have here is an apparent logical paradox:Any alteration of sequential change prevents the changes from returning to the inevitable track of the sequence they had previously been on. Yet all changes remain on the track of inevitability..

On the complexity issue, anon & T Parent: That's why I phrased the post in terms of "finite relevantly different possibilities". The view, as I understand it, is that as long as epsilon is finite for all the relevant properties in the space of possibilities, then the counterpart will be relevantly similar. As long as epsilon is finite though small, there should be a finite probability.

"The view, as I understand it, is that as long as epsilon is finite for all the relevant properties in the space of possibilities, then the counterpart will be relevantly similar." Wrong. Any change at all in the causal sequence will lead to a complete divergence of particulars.If you had left your home that day one second earlier or later, you would not have had the traffic accident that changed your life. The world may have later had wars for the same or similar reasons, but your unit, if any, would not have had the same personnel or casualties. Which would apply to any other unit ou would remotely have had dealings with. And on and on.

Anon: You need only choose epsilon small enough not to make any relevant difference over the whole of your life. One second isn't nearly small enough. All we need is *finite*. How about one googolplexth of a second? Furthermore, since my view allows scrambling, there only needs to be a finite probability of things working out in the intended way given that recurrence plus/minus epsilon.

Scott: Thanks for the Kundera reference. I read that back in college but I didn't recall that aspect of it (or really much else at all about it at this point). Maybe it shaped some of my thoughts about this, though.

On nihilism and all that: Your interpretation seems within the space of reasonable interpretations to me.

Eric, any difference at all is relevant, that's the point. Arbitrarily choosing a second or a nanosecond makes no difference where the point is that any change at all will be reflected in the irreversible sequence of change. Or do you somehow think that sequences are perfectly reversible? And do you think causation is somehow linear as well?

"The orthodox view is that you can unpour a cup of tea; it's just very unlikely."Apparently if they didn't teach academic philosophers about the laws of sequences in philosophy courses, they have difficulty thinking about the subject on their own. You, Eric, for example throw in some irrelevancy about entropy which again has completely missed the point.Non-academics ask questions about the subject. Why don't you? Do you suspect that somehow it's in the realm of the supernatural? In fact, it allows us to make some of our best arguments against such pseudoscientific malarkey.

Anon, this has degenerated into name-calling, and I suspect that you are the one who is in the wrong here. Please desist. If you wish to comment on future posts, I recommend that you present reasoned arguments rather than insults and pronouncements.

Eric, not once did I resort to name calling, unless any attempt to call you out is seen as name calling. You suspect I'm wrong? Is that the best you can do? I know you won't print this, but at least you'll read it.Ordinarily I wouldn't comment here at all, but this thing about the similarities of many worlds and the seriousness with which you take these ideas was just too much. Bye bye.

Anon, I think 'malarkey' might have been taken as name calling, but not necessarily against a person. I'm sure there's some things you find dear, perhaps particular movies or books, that wouldn't sit well with being called malarky. Perhaps imagine the language by which you'd prefer your own valued ideas critiqued and use that method.

If you two look again, you'll find that malarkey was not used in reference to anything that Eric said at all, but to the supernatural that he may suspect the sequentialists propose. Being a sequentialist myself, I hope I was not self-rude. But hope is the mother of self-deception so who knows.

Anon,shall we at least say - that if you did not intend to be rude, you are likely to achieve your intent better via presenting your arguments in a different way - at least in a civil forum like these comments.

You may have an interesting position, but you don't seem to have stated it clearly enough to be able to engage with it - or at least not added anything that can be engaged with after Nov 5 3:49.

Actually, Nietzsche tried to give a scientific explanation to eternal recurrence. Also, it seems that in each recurrence we don't have duplicates, but the same persons, which are recreated. Nietzsche wrote: "you will live again". But does eternal recurrence and the return of ourselves makes sense? Well, the second question is the most difficult to answer. I'll quote an explanation I found on another blog by a guy named ikurzgetsabsurd who replied to the blog's owner:

"First, for eternal recurrence to be possible, the universe must be eternal and the matter/energy in the universe must be in constant flux. If this is the case, every combination of matter and energy would be obligated to occur within the infinite scope of the universe. As you mentioned before, “we define the universe as everything.” Everything includes the pre-Big Bang singularity.

As we can see, something must have always existed. Even if the pre-Big Bang universe was nothing, as Lawrence Krauss says, it still has attractions, detractions and qualities. Which means that this ‘nothing’ still possesses extension, according to Galen Strawson.

We can also see, epistemically, that matter and energy is constantly changing. Leave an ice cube out for a little while.

If the universe is eternal in some form, and matter/energy is in constant flux, and there is a limited amount of matter (according to the principle of conservation) -- there would be a limited amount of combinations in an infinite universe. Therefore it requires that every possibility must occur and reoccur. Which is eternal recurrence.

Next, you say the recurrences of you wouldn’t be you, but would instead be clones. I disagree. Take the Ship of Theseus example. How many pieces can you replace on a ship and it still be the same ship? The same goes for the human body. Every atom in your physicality has been replaced, yet you are still you.

If we broke down the universe and rebuilt it exactly the same, you would still be you. If you are a physicalist (and I don’t know if you are) then the mental arises from the physical. Your mind is identical with your brain. If we rebuild your brain, your mind would be rebuilt too.

The only way that the next you wouldn’t be you is if some supernatural force implanted a new soul into you each recurrence. Instead, you are made up of the same material over and over again, and therefore, the same mind, the same identity, the same you would be recreated again and again and again.

And your last point. Yes I agree that time is property of the universe which was created at the instant of the Big Bang, before that no time existed, but something existed, even if that existence was nothing, which you will hear from Krauss.

Time being a property of the universe is not a problem for eternal recurrence. It would be a problem if time was an outside substance. If the universe dies and is reborn, then time dies and is reborn. Time, after all, is a property of the universe."

I agree with ikurzgetsabsurd: in recurrences which are the same, you still will be you, but without memories of previous recurrences. I know that identity is linked to memories, but I think we must distinguish between the identity and the self, the subjective point of view which experiences the memories. For example, a person with amnesia who loses his memories... is still him or a different person? Well, for Locke he would be a different person, but a lot of people don't agree to Locke. If the self is reduced to memories, then the person who had the old memories is dead and the amnesiac is a different person, but I think that is obviously wrong: even without his old memories, the amnesiac person is still the same self because his subjective point of view is the same.

Now, think about your future acts. Maybe tomorrow you're going to the cinema or maybe you'll read a book. The memories will not be the same. Does it mean that you will be a different person if you go to the cinema or read a book? Locke thought that. A person today will be a different person that the person of tomorrow, because the person of tomorrow will have memories that the person of today doesn't have. I don't think this is right. The "you" of today will be the same "you" of tomorrow because the subjective experiencer (you) will be the same, and the same applies if tomorrow you go to the cinema or read a book. Memories will be different, but the subjective experiencer is the same.

So, yes, in an eternal recurrence your subjective point of view will exist again, but without memories. Even then, if events repeat exactly, as times passes I will have the same memories as before. If Lock reduces the self to identity, and identity to memories, this means all "yous" in exact recurrences will be really "you". Essentially, you're not being copied: you are being rebuilt, just as a millionaire dismantles an ancient chateau in its original country and rebuilds it stone by stone in another country. In eternal recurrence, there is no even a change of "country" of your self. Maybe there is in a different combination of events, but we are talking about recurrences which are exact.

But we can think on a paradox that maybe goes against this (actually I think not, but it's a thought experiment). In an eternal recurring universe, all combinations repeat because the matter is finite and always the same. Suppose that a man had the technology to travel to a parallel universe before his origin universe enters a new cycle. He now lives in another universe. The origin universe enters a new cycle and an exact duplicate of the man is born, while the original man is still alive in the other universe. It's obvious the two men are different persons and have different subjective points of views even if they are the same physically. This means in eternal recurrence a new "you" will not be you. But this thought experiment has a lot of problems which indicate it's not valid:

- It takes for granted multiverse exist. It even takes for granted you can travel between universes.

- Most important: if the man travels to another universe before the original universe enters a new cycle, this means matter/energy in the new cycle will be less than in the previous one, because the man is missing in the new cycle, meaning that exact recurrences cannot happen again, so it's natutal that a new iteration of the subjective experierencer can't happen again. To make it happen, the origin universe will need to regain its lost matter. Suppose that another man from another univere whith the same mass as the original man travels to the original universe, thus restoring the original amount of mass/energy. Would that mean that exact iterations can repeat again? If yes, and the original man is still alive in other universe, another recurrence of a copy of him in the original universe would mean that the subjective experiencer always changes even between exact iterations, and the "self" or "subjective experiencer" is unique and can't repeat again. But even then, if a universe loses some amount of his original matter or energy due to inter-universes transference and then regains it due to the same cause, that would not mean that is the same universe as before losing its original matter/energy, explaining that a specific subjective experiencer can't happen again. In other words, in order to your "self" or "subjective experiencer" to repeat again and again, matter/energy can't escape or return to your universe, even if total matter/energy is constant.-Also, exchange of matter or energy between universes can be problematic for maintaining a cyclic eternal universe, and I doubt the universe allows for paradoxes.

Another consideration: if multiverse exists and there are a lot of exact copies of you, that means even if that persons have the same memories, they are not the same because they all exist at the same time, so each of them has his own subjective point of view. ¿Does that mean that if your own universe is cyclic, your "self" will not be recreated, and each exact recurrence will create a new subjective experiencer instead of the same "self"? I think not. The key point here is that copies of you in different universes are... in different universes. Maybe they are like you but their atoms, and the region of space-time is different, so it's logical that they are different persons. Think again of the chateau example. The rebuilt chateau is the same as before. We could build an exact copy of the chateau with different materials, but then it would be a copy.

And the famous Star Trek teleporters: some people think teleport kills you and make a copy with the same memories. This case would prove hard to Lock to solve. The point is: if the teleporter reads the state of the body and recreates it at destination, then the original person dies and a copy is created. If it transforms the body to energy, transports it to destination, and rebuilds the energy to the exact atoms as before, then that's exactly what it did: rebuild. The person has not died and is alive, but his conscioussness will not have memories of the travel because his brain didn't exist while he was energy. Technically, he was dead. He didn't exist. But he was rebuilt and exists again.

But is eternal return a possibility? Yes, it is. Today there are cosmological models which describe a cyclic universe.

From various entries from Wikipedia:

Eternal return (also known as "eternal recurrence") is a concept that the universe and all existence and energy has been recurring, and will continue to recur, in a self-similar form an infinite number of times across infinite time or space.

It is a purely physical concept, involving no supernatural reincarnation, but the return of beings in the same bodies. Time is viewed as being not linear but cyclical.

The basic premise proceeds from the assumption that the probability of a world coming into existence exactly like our own is greater than zero (we know this because our world exists). If space and time are infinite, then logic follows that our existence must recur an infinite number of times.

In 1871 Louis Auguste Blanqui, assuming a Newtonian cosmology where time and space are infinite, claimed to have demonstrated eternal recurrence as a mathematical certainty. In the post-Einstein period researchers cast doubts on the idea that time or space was in fact infinite, but many models provided the notion of spatial or temporal infinity required by the eternal-return hypothesis.

The oscillatory universe model in physics offers an example of how the universe may cycle through the same events infinitely. Arthur Eddington's concept "arrow of time", for example, discusses cosmology as proceeding up to a certain point, after which it undergoes a time reversal (which, as a consequence of T-symmetry, is thought to bring about a chaotic state due to entropy). Stephen Hawking and J. Richard Gott have also proposed models by which a universe could undergo time travel, provided the balance between mass and energy created the appropriate cosmological geometry.

Multiverse hypotheses in physics describe models where space or time is infinite, although local universes with their own big bangs could be finite space-time bubbles.

While the big bang theory in the framework of relativistic cosmology seems to be at odds with eternal return, there are now many different speculative big bang scenarios in quantum cosmology which actually imply eternal return - although based on other assumptions than Nietzsche's. So there are competing models and hypotheses with a temporal, spatial or spatio-temporal eternal return of everything in all variations as Nietzsche has envisaged.

The oscillating universe theory—that the universe will end in a collapse or 'big crunch' followed by another big bang, and so on—dates from 1930. Cosmologists such as professor Alexander Vilenkin from Tufts University and Massachusetts Institute of Technology professor Max Tegmark suggest that if space is sufficiently large and uniform, or infinite as some theories suggest, and if quantum theory is true such that there is only a finite number of configurations within a finite volume possible, due to Heisenberg's uncertainty principle, then identical instances of the history of Earth's entire Hubble volume occur every so often, simply by chance. Tegmark calculates that our nearest so-called doppelgänger, is 1010115 meters away from us (a double exponential function larger than a googolplex). In principle, it would be impossible to scientifically verify an identical Hubble volume. However, it does follow as a fairly straightforward consequence from otherwise unrelated scientific observations and theories. Tegmark suggests that statistical analyses exploiting the anthropic principle provide an opportunity to test multiverse theories in some cases. Generally, science would consider a multiverse theory that posits neither a common point of causation, nor the possibility of interaction between universes, to be an ideal speculation. However, it is a fundamental assumption of cosmology that the universe continues to exist beyond the scope of the observable universe, and that the distribution of matter is everywhere the same at such a large scale (see cosmological principle).

Nietzsche scholar Walter Kaufmann has described an argument originally put forward by Georg Simmel, which rebuts the claim that a finite number of states must repeat within an infinite amount of time:

Even if there were exceedingly few things in a finite space in an infinite time, they would not have to repeat in the same configurations. Suppose there were three wheels of equal size, rotating on the same axis, one point marked on the circumference of each wheel, and these three points lined up in one straight line. If the second wheel rotated twice as fast as the first, and if the speed of the third wheel was 1/π of the speed of the first, the initial line-up would never recur.

Thus a system could have an infinite number of distinct physical configurations that never recur. However the example presupposes the possibility of perfect continuity: for instance, if the universe proves to have a quantum foam nature, then the exact quantity of an irrational number cannot be expressed by any physical object.

A cyclic model (or oscillating model) is any of several cosmological models in which the universe follows infinite, or indefinite, self-sustaining cycles. For example, the oscillating universe theory briefly considered by Albert Einstein in 1930 theorized a universe following an eternal series of oscillations, each beginning with a big bang and ending with a big crunch; in the interim, the universe would expand for a period of time before the gravitational attraction of matter causes it to collapse back in and undergo a bounce.

One new cyclic model is a brane cosmology model of the creation of the universe, derived from the earlier ekpyrotic model. It was proposed in 2001 by Paul Steinhardt of Princeton University and Neil Turok of Cambridge University. The theory describes a universe exploding into existence not just once, but repeatedly over time. The theory could potentially explain why a repulsive form of energy known as the cosmological constant, which is accelerating the expansion of the universe, is several orders of magnitude smaller than predicted by the standard Big Bang model.

A different cyclic model relying on the notion of phantom energy was proposed in 2007 by Lauris Baum and Paul Frampton of the University of North Carolina at Chapel Hill.

I support cyclic models because I think It has more sense to think of a cyclic universe than an universe with a beginning and end. If before the Big Bang space and time didn't exit... what was the cause for the Big Bang? Also, as Wikipedia explains, the fact that our universe exists means that the probability of existing is greater than zero. And I add: the fact that our "selves", our subjective point of views exist means that the probability of our "selves" to exist is greater than zero. Which means that is logical to think that our universe will exist again and our subjective points of view will also exist again, along with other different combinations. Also, if the models which speak of the universe traveling back in time are true, they further support the idea that the recurrent iterations of ourselves are really ourselves, and not copies with a new subjective point of view. Think of a DVD. You can watch the film and when it ends you can play it again, but the film is always the same.

@ TParentdeleting all the 3's from pi removes it from the class of deterministic dynamical systems with finite volume state spaces from whence it would have had to sprang, uh, sprung. Poincarés theorem only applies to systems which are like Hamiltonian dynamics in the sense that they are continuous, deterministic, finite volume state space, and have an invariant measure do determine that volume. The eternal return would no longer be true in some kind of infinite-number-of-degrees-of-freedom limit of such systems. This is implicitly what underlies Boltzmann's derivation of the 2nd Law, as a probabilistic law, from Hamiltonian dynamics, which is deterministic and subject to Poincaré. I take it that this is how probabilities arise: only from this passage to a limit beyond the scope of Poincaré recurrence. See my new book on Hilbert's Sixth Problem on Amazon dot com (Lambert Academic Publishing).